-15x^2+16x+1=0

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Solution for -15x^2+16x+1=0 equation: 


Simplifying
-15x2 + 16x + 1 = 0

Reorder the terms:
1 + 16x + -15x2 = 0

Solving
1 + 16x + -15x2 = 0

Solving for variable 'x'.

Begin completing the square.  Divide all terms by
-15 the coefficient of the squared term: 

Divide each side by '-15'.
-0.06666666667 + -1.066666667x + x2 = 0

Move the constant term to the right:

Add '0.06666666667' to each side of the equation.
-0.06666666667 + -1.066666667x + 0.06666666667 + x2 = 0 + 0.06666666667

Reorder the terms:
-0.06666666667 + 0.06666666667 + -1.066666667x + x2 = 0 + 0.06666666667

Combine like terms: -0.06666666667 + 0.06666666667 = 0.00000000000
0.00000000000 + -1.066666667x + x2 = 0 + 0.06666666667
-1.066666667x + x2 = 0 + 0.06666666667

Combine like terms: 0 + 0.06666666667 = 0.06666666667
-1.066666667x + x2 = 0.06666666667

The x term is -1.066666667x.  Take half its coefficient (-0.5333333335).
Square it (0.2844444446) and add it to both sides.

Add '0.2844444446' to each side of the equation.
-1.066666667x + 0.2844444446 + x2 = 0.06666666667 + 0.2844444446

Reorder the terms:
0.2844444446 + -1.066666667x + x2 = 0.06666666667 + 0.2844444446

Combine like terms: 0.06666666667 + 0.2844444446 = 0.35111111127
0.2844444446 + -1.066666667x + x2 = 0.35111111127

Factor a perfect square on the left side:
(x + -0.5333333335)(x + -0.5333333335) = 0.35111111127

Calculate the square root of the right side: 0.592546295

Break this problem into two subproblems by setting 
(x + -0.5333333335) equal to 0.592546295 and -0.592546295.


Subproblem 1
x + -0.5333333335 = 0.592546295

Simplifying
x + -0.5333333335 = 0.592546295

Reorder the terms:
-0.5333333335 + x = 0.592546295

Solving
-0.5333333335 + x = 0.592546295

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '0.5333333335' to each side of the equation.
-0.5333333335 + 0.5333333335 + x = 0.592546295 + 0.5333333335

Combine like terms: -0.5333333335 + 0.5333333335 = 0.0000000000
0.0000000000 + x = 0.592546295 + 0.5333333335
x = 0.592546295 + 0.5333333335

Combine like terms: 0.592546295 + 0.5333333335 = 1.1258796285
x = 1.1258796285

Simplifying
x = 1.1258796285


Subproblem 2
x + -0.5333333335 = -0.592546295

Simplifying
x + -0.5333333335 = -0.592546295

Reorder the terms:
-0.5333333335 + x = -0.592546295

Solving
-0.5333333335 + x = -0.592546295

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '0.5333333335' to each side of the equation.
-0.5333333335 + 0.5333333335 + x = -0.592546295 + 0.5333333335

Combine like terms: -0.5333333335 + 0.5333333335 = 0.0000000000
0.0000000000 + x = -0.592546295 + 0.5333333335
x = -0.592546295 + 0.5333333335

Combine like terms: -0.592546295 + 0.5333333335 = -0.0592129615
x = -0.0592129615

Simplifying
x = -0.0592129615


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.1258796285, -0.0592129615}

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